Riemann problems for the nonhomogeneous Aw-Rascle model

Abstract

In this paper the celebrated second order Aw-Rascle nonhomogeneous system describing traffic flows is considered. Within the framework of the method of differential constraints, a suitable reduction procedure is developed for solving a class of Riemann problems which are of interest in traffic flows theory. In particular, for a given source term, we find the general solution of the Riemann problem in terms of shock waves, contact discontinuities and generalized rarefaction waves. The interaction between a shock wave and a generalized rarefaction wave is also studied and a related generalized Riemann problem is solved. Numerical results are in agreement with the exact analytical solution.